Listening for gist requires students to listen to a text and to understand the general idea of what is conveyed without paying too much attention to individual words and phrases. For example, students listen to a conversation and decide if the speakers are agreeing or disagreeing on where to spend the evening. Listening for specific information is where students are asked to listen for details. For example, What time does the film start? What sort of restaurant does speaker A want to go to? Does speaker B prefer an Indian or a Spanish restaurant?
It is difficult for me to say what the objectives are for listen and point, listen and do, listen and number the picture; I would be happy to do this if you could give me more information. Take the following example: you show students photographs of a beach scene, a mountain scene and a busy city street; you then ask them to listen to a description of one of the pictures and point to the correct picture. Here the objective is listening for gist. Listening for specific information is the objective if the pictures are very similar - for example, you ask students to listen and decide which picture is being described, the choice is between a picture where a group of people are sunbathing on the beach, a group are playing football on the beach and a group are playing tennis on the beach.
Please write in again with exact details of the tasks and I will be able to give you more assistance.